The growth rate of wind-turbine wakes in the atmospheric boundary layer is a key parameter in analytical models used to predict wind-turbine wakes and their effects in wind farms. To date, the turbine-wake growth rate is determined empirically, owing to our limited understanding of the physical mechanisms leading to the recovery of the wakes in turbulent flows. Here, a simple physically-based model for wind-turbine wake growth is proposed based on the analogy with scalar dispersion in turbulent flows. The model is developed based on Taylor's diffusion theory and intrinsically accounts for the effect of ambient turbulence intensity. In validations against large-eddy simulations of the wake flow of a turbine under different inflow turbulence conditions, it is found that the model yields good predictions of the growth of the turbine wakes. A slight underestimation of the wake growth rate is found only in the lowest ambient turbulence case, due to the non-negligible contribution of the turbine-induced turbulence in that case.